I climbed Mt Tongariro, I had to put alot of energy in to get to the summit. 

The earth itself had to transform a lot of energy to create Mt Tongariro. 

The Helicopter that takes Fabio Wibmer to the top of his Mountain Bike ride transformed alot of chemical potential energy into kinetic energy and then into gravitational potential energy. 

To lift my dog up, I had to transform chemical potential energy into kinetic energy and this energy into gravitational potential energy. 

But how much did I transform? How much energy does Zed have when he is 2 meters above the ground? How much Gravitational Potential Energy does he have?

Gravitational Potential Energy  = mass * gravity * height

Ep = m g h

Let's take Zed and myself. 

Zed's mass is 20kg, mine is 75kg. The table is 1 meter high

How much GPE do we both have while standing on the table?

1. Zed's GPE 

GPE = m g h

GPE = 20kg x 9.81ms-2 x 1m

Zeds GPE = 196 Joules

2. Mr Cowley's GPE

GPE = m g h

GPE = 75kg x 9.81ms-2  x  1m

GPE = 736 Joules

Then, what is Zed's GPE when I lift him so that he is 3 meters above the ground?

3. Zed lifted by Mr Cowley

GPE = m g h

GPE = 20kg x 9.81ms-2 x 3m

Zeds GPE = 589 Joules

That's a lot of energy for Zeds bones and joints to transform into elastic energy (bend without snapping). No wonder he doesn't want me to drop him from way up there.

We can calculate that by taking 3 factors

Mass - how massive is the object (kg)

Gravity - with how gravity is on that planet (ms-2 )

Height - how far above the other surface is something (m)

As we can see from this, how much mass something has matters. If I was lifting my big dog Luka up, then, as he is more massive, he would have more gravitational potential energy

Gravity matters as well, if we are on the moon, then jumping from 2 or 3 meters would be fun as there would be little ground shock

On Earth gravity has a value of 9.81ms-2 

However, you can round gravity to 10ms-2 

Height relative to a surface matters. Notice that it is not height relative to the ground. If I lift up Zed and I drop him on the table, that would be very different to dropping him onto the ground. He his closer to the table, so the height relative to the table is less, thus he has less fall time, his velocity will be less and thus so too will be his impact. So, when calculating height it is relative to a surface. If you are in the Skytower and jump and land on the same floor, because you are still inside, then you wont suddenly splatter on the floor. Even though, relative to the earth outside, your GPE is huge. 

Mass, Gravity and Height.... Times these together and you get the objects Gravitational Potential Energy

Gravitational Potential Energy  = mass * gravity * height

Ep = m g h

Note, GPE is often written as Energy potential, or Ep = mgh

This is because it is a very common calculation, so common that by dropping the G everyone still knows that the calculation is for GPE. And if you forget that Ep = GPE, thats ok because the g is in the other side of the formula :-)

Mr Cowley Lecture - Weight, Mass and Gravity

The bigger you are the harder it is to stop you

In other words, the greater the mass, the greater the Kinetic Energy

Also, the Faster you are going, or the higher your Velocity the harder it is to stop you 

In other words, the greater the velocity the greater the Kinetic Energy

But what matters more, velocity or size?

Well, it's relative; if a bullet hits you, you can die, but if you are hit by a train, you can also die. Let's have a look at two things that are similar in size: a bullet and a rock, as explained by Adam Savage from Mythbusters

Kinetic Energy, or Energy Kinetic is the same thing

It is written as EK, Ek,  Ek Ek, or even KE

With this we take the two things that matter; the mass of the object and how fast it is moving

Mass is not nearly as important as how fast something is moving, that is why a  bullet is so deadly

Because velocity is so very important, we will square it:  v2

Because mass is not nearly as important we will half it: ½m

This makes our equation; 

Kinetic Energy Equals = half mass times velocity squared

Kinetic Energy is in Joules

Mass is in Kilograms

Velocity is in meters per second

We can write this as Ek = ½ mass * velocity2  

When something falls, it speeds up

If a ball is at the top of a cliff and is then pushed off, at the top of the cliff it has maximum GPE, as it falls it gets closer to the ground, so it has less GPE, but it gets faster so it gets more EK. In the moment before it hits the ground it is at its maximum velocity, so almost all of the energy is converted into Ek and there is almost no GPE is left

Calculating Velocity when only given GPE information

Ep = m*g*h

Ek =½ *m* v2

Energy is Energy, so Ep is equal to Ek

Ep = Ek

This means that the energy that an object has before it falls from a height, will be the same as the amount of energy that object has when it hits the ground

m*g*h = ½ *m* v2

If we cancel 'm' as its on both side of the equation, then

g*h = ½ v2     

Then we can rearrange to use Ep information to calculate the expected velocity if an object falls

2*g*h = v2  

√(2*g*h) = v  

This will give a theoretical velocity. 

Thus, when given a height we can calculate the Velocity the object will be going when it gets to '0' height. This is summarized below in bold

Velocity when dropped from a given height:

√(2*g*h) = v  

Or if we round g to 10 then 2x 10 is 20 so:

√(20*h) = v  

The actual velocity will be less due to air resistance. Air resistance causes some of the energy to transform into heat energy